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We expose in a tutorial fashion the mechanisms which underlie the synthesis of optimization algorithms based on dynamic integral quadratic constraints. We reveal how these tools from robust control allow to design accelerated gradient…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
This study presents a population-based evolutionary optimization algorithm (Adaptive Differential Evolution with Diversification Strategies or ADEDS). The algorithm developed using the sinusoidal objective function and subsequently…
Evolutionary algorithms are wildly used in unmanned aerial vehicle path planning for their flexibility and effectiveness. Nevertheless, they are so sensitive to the change of environment that can't adapt to all scenarios. Due to this…
We have derived the perimeter generating function of a model of punctured staircase polygons in which the internal staircase polygon is rotated by a 90degree angle with respect to the outer staircase polygon. In one approach we calculated a…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
In this paper, we present a novel optimization-based framework for autonomous excavator trajectory generation under various objectives, including minimum joint displacement and minimum time. Traditional methods on excavation trajectory…
Recent progress in 3D/4D scene generation emphasizes the importance of physical alignment throughout video generation and scene reconstruction. However, existing methods improve the alignment separately at each stage, making it difficult to…
This paper presents a novel partial differential equation (PDE)-based framework for controlling an ensemble of robots, which have limited sensing and actuation capabilities and exhibit stochastic behaviors, to perform mapping and coverage…
Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting…
Effective trajectory generation is essential for reliable on-board spacecraft autonomy. Among other approaches, learning-based warm-starting represents an appealing paradigm for solving the trajectory generation problem, effectively…
Mathematical formulations of real world optimization studies frequently present characteristics such as non-linearity, discontinuity and high complexity. This class of problems may also exhibit a high number of global minimum/maximum…
In swarm intelligence, Particle Swarm Optimization (PSO) and Differential Evolution (DE) have been successfully applied in many optimization tasks, and a large number of variants, where novel algorithm operators or components are…
Recent advancements in data-driven approaches, such as Neural Operator (NO), have demonstrated their effectiveness in reducing the solving time of Partial Differential Equations (PDEs). However, one major challenge faced by these approaches…
Two meta-evolutionary optimization strategies described in this paper accelerate the convergence of evolutionary programming algorithms while still retaining much of their ability to deal with multi-modal problems. The strategies, called…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
In this work, we introduce SPADE, a path planning framework designed for autonomous navigation in dynamic environments using 3D scene graphs. SPADE combines hierarchical path planning with local geometric awareness to enable collision-free…
In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…